| output gate | \gamma_\rho | N | distance | cited |
|---|---|---|---|---|
| \mathrm{CS}_{01}\cdot \mathrm{CS}_{23}\cdot \mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{023}\cdot \mathrm{CCZ}_{134} | — | 11 | d = 3 | Wills et al. (2026) |
| \mathrm{CS}_{01}\cdot \mathrm{CS}_{34}\cdot \mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{023}\cdot \mathrm{CCZ}_{234} | — | 11 | d = 3 | Wills et al. (2026) |
| \mathrm{CS}_{01}\cdot \mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{034} | — | 11 | d = 3 | Wills et al. (2026) |
| \mathrm{CS}_{01}\cdot \mathrm{CS}_{34}\cdot \mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{234} | — | 11 | d = 3 | Wills et al. (2026) |
| \mathrm{CS}_{01}\cdot \mathrm{CCZ}_{023}\cdot \mathrm{CCZ}_{124} | — | 11 | d = 3 | Gong et al. (2026) |
| \mathrm{CS}_{01}\cdot \mathrm{CS}_{24}\cdot \mathrm{CCZ}_{023} | — | 11 | d = 3 | Wills et al. (2026) |
| \mathrm{T}_{0}\cdot \mathrm{CS}_{01}\cdot \mathrm{CS}_{23}\cdot \mathrm{CCZ}_{234} | — | 12 | d = 3 | Wills et al. (2026) |
These factories share n, k and d but prepare different magic states. No CNOT circuit with S, Z and CZ corrections turns one of these gates into another.
Same n and k at other distances: [\![48,\,5,\,4]\!]
Nearest lengths with the same k and d: [\![47,\,5,\,3]\!] · [\![51,\,5,\,3]\!] · [\![44,\,5,\,3]\!] · [\![52,\,5,\,3]\!] · [\![43,\,5,\,3]\!] · [\![53,\,5,\,3]\!] · [\![55,\,5,\,3]\!] · [\![40,\,5,\,3]\!] · [\![39,\,5,\,3]\!] · [\![57,\,5,\,3]\!] · [\![59,\,5,\,3]\!] · [\![60,\,5,\,3]\!]